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Journal articles on the topic 'Lagrange equations'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

Derevenskii, V. P. "Lagrange matrix equations." Russian Mathematics 59, no. 12 (November 7, 2015): 10–20. http://dx.doi.org/10.3103/s1066369x15120026.

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2

Potts, Renfrey B. "Discrete Lagrange equations." Bulletin of the Australian Mathematical Society 37, no. 2 (April 1988): 227–33. http://dx.doi.org/10.1017/s0004972700026769.

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3

Koh, Youngmee, and Sangwook Ree. "Lagrange and Polynomial Equations." Journal for History of Mathematics 27, no. 3 (June 30, 2014): 165–82. http://dx.doi.org/10.14477/jhm.2014.27.3.165.

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4

Ellis, David C. P., François Gay-Balmaz, Darryl D. Holm, and Tudor S. Ratiu. "Lagrange–Poincaré field equations." Journal of Geometry and Physics 61, no. 11 (November 2011): 2120–46. http://dx.doi.org/10.1016/j.geomphys.2011.06.007.

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5

Baev, V. K. "Lagrange Equations of Envelopes." Journal of Physics: Conference Series 941 (December 2017): 012087. http://dx.doi.org/10.1088/1742-6596/941/1/012087.

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6

Mingliang, Zheng. "RENORMALIZATION GROUP METHOD FOR A CLASS OF LAGRANGE MECHANICAL SYSTEMS." Journal of the Serbian Society for Computational Mechanics 16, no. 2 (December 1, 2022): 96–104. http://dx.doi.org/10.24874/jsscm.2022.16.02.07.

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Considering the important role of small parameter perturbation term in mechanical systems, the perturbed dynamic differential equations of Lagrange systems are established. The basic idea and method of solving ordinary differential equations by normal renormalization group method are transplanted into a kind of Lagrange mechanical systems, the renormalization group equations of Euler-Lagrange equations are obtained, and the first-order uniformly valid asymptotic approximate solution of Lagrange systems with a single-degree-of-freedom is given. Two examples are used to show the calculation steps of renormalization group method in detail as well as to verify the correctness of the method. The innovative finding of this paper is that for integrable Lagrange systems, its renormalization group equations are also integrable and satisfy the Hamilton system's structure.
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7

Sun, Lanyin, and Chungang Zhu. "B-Spline Solutions of General Euler-Lagrange Equations." Mathematics 7, no. 4 (April 22, 2019): 365. http://dx.doi.org/10.3390/math7040365.

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The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline solutions to general Euler-Lagrange equations are given. As part of this work, we present a general method for generating B-spline solutions of the second- and fourth-order Euler-Lagrange equations. Furthermore, we show that some existing techniques for surface design, such as Coons patches, are exactly the special cases of the generalized Partial differential equations (PDE) surfaces with appropriate choices of the constants.
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8

Nowakowski, Andrzej, and Andrzej Rogowski. "Periodic solutions of Lagrange equations." Topological Methods in Nonlinear Analysis 22, no. 1 (September 1, 2003): 167. http://dx.doi.org/10.12775/tmna.2003.034.

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9

Herzallah, Mohamed A. E., and Dumitru Baleanu. "Fractional Euler–Lagrange equations revisited." Nonlinear Dynamics 69, no. 3 (January 18, 2012): 977–82. http://dx.doi.org/10.1007/s11071-011-0319-5.

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10

Burov, A. A., and I. I. Kosenko. "The Lagrange differential-algebraic equations." Journal of Applied Mathematics and Mechanics 78, no. 6 (2014): 587–98. http://dx.doi.org/10.1016/j.jappmathmech.2015.04.006.

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11

Constantinescu, Oana A., and Ebtsam H. Taha. "Alternative Lagrangians obtained by scalar deformations." International Journal of Geometric Methods in Modern Physics 17, no. 04 (March 2020): 2050050. http://dx.doi.org/10.1142/s0219887820500504.

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We study mechanical systems that can be recast into the form of a system of genuine Euler–Lagrange equations. The equations of motions of such systems are initially equivalent to the system of Lagrange equations of some Lagrangian [Formula: see text], including a covariant force field. We find necessary and sufficient conditions for the existence of a differentiable function [Formula: see text] such that the initial system is equivalent to the system of Euler–Lagrange equations of the deformed Lagrangian [Formula: see text].
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12

Bodaghi, Abasalt, Hossein Moshtagh, and Amir Mousivand. "Characterization and Stability of Multi-Euler-Lagrange Quadratic Functional Equations." Journal of Function Spaces 2022 (October 10, 2022): 1–9. http://dx.doi.org/10.1155/2022/3021457.

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The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagrange quadratic mappings. In other words, it reduces a system of equations defining the multi-Euler-Lagrange quadratic mappings to an equation, say, the multi-Euler-Lagrange quadratic functional equation. Moreover, some results corresponding to known stability (Hyers, Rassias, and Gӑvruta) outcomes regarding the multi-Euler-Lagrange quadratic functional equation are presented in quasi- β -normed and Banach spaces by using the fixed point methods. Lastly, an example for the nonstable multi-Euler-Lagrange quadratic functional equation is indicated.
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13

Yuan, Xiaoping. "Lagrange stability for asymmetric Duffing equations." Nonlinear Analysis: Theory, Methods & Applications 43, no. 2 (January 2001): 137–51. http://dx.doi.org/10.1016/s0362-546x(99)00170-4.

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14

Grabowska, Katarzyna, Janusz Grabowski, and Paweł Urbański. "AV-differential geometry: Euler–Lagrange equations." Journal of Geometry and Physics 57, no. 10 (September 2007): 1984–98. http://dx.doi.org/10.1016/j.geomphys.2007.04.003.

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15

Kikuchi, Keiichi. "EXTENDED HARMONIC MAPS AND LAGRANGE EQUATIONS." JP Journal of Geometry and Topology 20, no. 1 (May 6, 2017): 39–60. http://dx.doi.org/10.17654/gt020010039.

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16

Shen, Jianhua, Lu Chen, and Xiaoping Yuan. "Lagrange stability for impulsive Duffing equations." Journal of Differential Equations 266, no. 11 (May 2019): 6924–62. http://dx.doi.org/10.1016/j.jde.2018.11.022.

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17

Yuan, Xiaoping. "Lagrange Stability for Duffing-Type Equations." Journal of Differential Equations 160, no. 1 (January 2000): 94–117. http://dx.doi.org/10.1006/jdeq.1999.3663.

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18

Djukic, Djordje. "Generalized Lagrange-D’Alembert principle." Publications de l'Institut Math?matique (Belgrade) 91, no. 105 (2012): 49–58. http://dx.doi.org/10.2298/pim1205049d.

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The major issues in the analysis of the motion of a constrained dynamic system are to determine this motion and calculate constraint forces. In the analytical mechanics, only the first of the two problems is analyzed. Here, the problem is solved simultaneously using: 1) Principle of liberation of constraints; 2) Principle of generalized virtual displacement; 3) Idea of ideal constraints; 4) Concept of generalized and ?supplementary" generalized coordinates. The Lagrange-D?Alembert principle of virtual work is generalized introducing virtual displacement as vectorial sum of the classical virtual displacement and virtual displacement in the ?supplementary" directions. From such principle of virtual work we derived Lagrange equations of the second kind and equations of dynamical equilibrium in the ?supplementary" directions. Constrained forces are calculated from the equations of dynamic equilibrium. At the same time, this principle can be used for consideration of equilibrium of system of material particles. This principle simultaneously gives the connection between applied forces at equilibrium state and the constrained forces. Finally, the principle is applied to a few particular problems.
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19

Hasan, Eyad Hasan. "Fractional Variational Problems of Euler-Lagrange Equations with Holonomic Constrained Systems." Applied Physics Research 8, no. 3 (April 23, 2016): 60. http://dx.doi.org/10.5539/apr.v8n3p60.

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<p class="1Body">In this paper, we examined the fractional Euler-Lagrange equations for Holonomic constrained systems. The Euler-Lagrange equations are derived using the fractional variational problem of Lagrange. In addition, we achieved that the classical results were obtained are agreement when fractional derivatives are replaced with the integer order derivatives. Two physical examples are discussed to demonstrate the formalism.</p>
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20

Fu, Jing-Li, Lijun Zhang, Chaudry Khalique, and Ma-Li Guo. "Circulatory integral and Routh's equations of Lagrange systems with Riemann-Liouville fractional derivatives." Thermal Science 25, no. 2 Part B (2021): 1355–63. http://dx.doi.org/10.2298/tsci200520034f.

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In this paper, the circulatory integral and Routh?s equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, and the circulatory integral of Lagrange systems is obtained by making use of the relationship between Riemann-Liouville fractional integrals and fractional derivatives. Thereafter, the Routh?s equations of Lagrange systems are given based on the fractional circulatory integral. Two examples are presented to illustrate the application of the results.
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21

DUAN, ZHISHENG, JINZHI WANG, RONG LI, and LIN HUANG. "A GENERALIZATION OF SMOOTH CHUA'S EQUATIONS UNDER LAGRANGE STABILITY." International Journal of Bifurcation and Chaos 17, no. 09 (September 2007): 3047–59. http://dx.doi.org/10.1142/s0218127407018853.

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In this paper, smooth Chua's equation is generalized to a higher order system from a special viewpoint of interconnected systems. Simple conditions for Lagrange stability are established. And a detailed Lagrange stable region analysis is given for the canonical Chua's oscillator. In addition, a new nonlinearly coupled Chua's circuit that appeared in the recent literature is also discussed and a Lagrange stability condition is presented. Several examples are presented to illustrate the results.
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22

Zhang, Xiang Mei, An Ping Xu, and Xian Zhou Guo. "Stability Analysis of Fractional Delay Differential Equations by Lagrange Polynomial." Advanced Materials Research 500 (April 2012): 591–95. http://dx.doi.org/10.4028/www.scientific.net/amr.500.591.

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The paper deals with the numerical stability analysis of fractional delay differential equations with non-smooth coefficients using the Lagrange collocation method. In this paper, based on the Grunwald-Letnikov fractional derivatives, we discuss the approximation of fractional differentiation by the Lagrange polynomial. Then we study the numerical stability of the fractional delay differential equations. Finally, the stability of the delayed Mathieu equation of fractional order is studied and examined by Lagrange collocation method.
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23

Gorobtsov, Alexander, Oleg Sychev, Yulia Orlova, Evgeniy Smirnov, Olga Grigoreva, Alexander Bochkin, and Marina Andreeva. "Optimal Greedy Control in Reinforcement Learning." Sensors 22, no. 22 (November 18, 2022): 8920. http://dx.doi.org/10.3390/s22228920.

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We consider the problem of dimensionality reduction of state space in the variational approach to the optimal control problem, in particular, in the reinforcement learning method. The control problem is described by differential algebraic equations consisting of nonlinear differential equations and algebraic constraint equations interconnected with Lagrange multipliers. The proposed method is based on changing the Lagrange multipliers of one subset based on the Lagrange multipliers of another subset. We present examples of the application of the proposed method in robotics and vibration isolation in transport vehicles. The method is implemented in FRUND—a multibody system dynamics software package.
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24

MANOFF, S. "EINSTEIN'S THEORY OF GRAVITATION AS A LAGRANGIAN THEORY FOR TENSOR FIELDS." International Journal of Modern Physics A 13, no. 12 (May 10, 1998): 1941–67. http://dx.doi.org/10.1142/s0217751x98000846.

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Einstein's theory of gravitation (ETG) is considered as a Lagrangian theory of tensor fields over (pseudo) Riemannian spaces without torsion (Vn spaces, n=4) by means of the method of Lagrangians with covariant derivarives (MLCD). In a trivial manner Euler–Lagrange's equations as Einstein's equations are obtained. The corresponding energy–momentum tensors (EMT's) are found for the standard for the ETG Lagrangian invariant on the basis of the covariant Noether identities. The symmetric energy–momentum tensor of Hilbert appears as an element irrelevant to the whole scheme of the considered Lagrangian thoery of tensor fields over Vn spaces despite of the fact that it has some elements of the structure of the variational EMT of Euler–Lagrange. The notion of the active gravitational rest mast density is related to the variational EMT of Euler–Lagrange and on this basis to a certain extent to the EMT of Hilbert.
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25

Wang, Zhao Qing, Jian Jiang, Bing Tao Tang, and Wei Zheng. "Numerical Solution of Bending Problem for Elliptical Plate Using Differentiation Matrix Method Based on Barycentric Lagrange Interpolation." Applied Mechanics and Materials 638-640 (September 2014): 1720–24. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1720.

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A differentiation matrix method based on barycentric Lagrange interpolation for numerical analysis of bending problem for elliptical plate is presented. Embedded the elliptical domain into a rectangular, the barycentric Lagrange interpolation in tensor form is used to approximate unknown function. The governing equation of bending plate is discretized by the differentiation matrix derived from barycentric Lagrange interpolation to form a system of algebraic equations. The boundary conditions on curved boundary are directly discretized using barycentric Lagrange interpolation. Combining discrete algebraic equations of governing equation and boundary conditions to form an over-constraints system of equations, the numerical solutions on rectangular can be obtained by solving it. Then, the numerical solutions on elliptical domain are obtained by interpolating the data on rectangular. Numerical results of elliptical plate with uniform load illustrate the effectiveness and accuracy of the proposed method.
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26

Agrawal, Sunil K., Pana Claewplodtook, and Brian C. Fabien. "Optimal Trajectories of Open-Chain Robot Systems: A New Solution Procedure Without Lagrange Multipliers." Journal of Dynamic Systems, Measurement, and Control 120, no. 1 (March 1, 1998): 134–36. http://dx.doi.org/10.1115/1.2801309.

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For an n d.o.f. robot system, optimal trajectories using Lagrange multipliers are characterized by 4n first-order nonlinear differential equations with 4n boundary conditions at the two end time. Numerical solution of such two-point boundary value problems with shooting techniques is hard since Lagrange multipliers can not be guessed. In this paper, a new procedure is proposed where the dynamic equations are embedded into the cost functional. It is shown that the optimal solution satisfies n fourth-order differential equations. Due to absence of Lagrange multipliers, the two-point boundary-value problem can be solved efficiently and accurately using classical weighted residual methods.
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27

Wu, Guo-Cheng. "Variational Iteration Method forq-Difference Equations of Second Order." Journal of Applied Mathematics 2012 (2012): 1–5. http://dx.doi.org/10.1155/2012/102850.

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Recently, Liu extended He's variational iteration method to strongly nonlinearq-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. Theq-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.
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28

Askerov, I. "Approximate method of solving one periodic optimal regulated boundary value problem." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 2 (2019): 66–69. http://dx.doi.org/10.17721/1812-5409.2019/2.7.

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In the present work we considered the solution of one periodic optimal regulated boundary value problem by the asymptotic method. For the solution of the problem with extended functional writing, boundary conditions and Euler-Lagrange equations were found. The approach to the solution of the problem depending on a small parameter by seeking a system of nonlinear differential equations and solving Euler-Lagrange equations, the solution of the general problem in the first approach comes down to solving two nonlinear algebraic equations.
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29

Wcislik, Miroslaw, and Karol Suchenia. "Holonomicity analysis of electromechanical systems." Open Physics 15, no. 1 (December 29, 2017): 942–47. http://dx.doi.org/10.1515/phys-2017-0115.

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Abstract Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange - d’Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.
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30

Herzallah, Mohamed A. E., and Dumitru Baleanu. "Fractional-order Euler–Lagrange equations and formulation of Hamiltonian equations." Nonlinear Dynamics 58, no. 1-2 (March 18, 2009): 385–91. http://dx.doi.org/10.1007/s11071-009-9486-z.

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31

Vol’nikov, Mikhail, and Vladimir Vasilevich Smogunov. "Friction accounting in mathematical models of dissipative systems." Vestnik of Astrakhan State Technical University. Series: Management, computer science and informatics 2022, no. 2 (April 29, 2022): 110–18. http://dx.doi.org/10.24143/2072-9502-2022-2-110-118.

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Obtaining models of mechanical processes with dissipation based on the Euler-Lagrange theory has undoubted advantages over Newton's theory due to the smaller size of the considered vector of variables included in the equations. However, the Euler-Lagrange variation theory is not applicable to the description of the motion of systems with dissipation. The aim of the work is to demonstrate the possibility of using the Euler-Lagrange theory in relation to dissipative systems with different types of friction. Mathematical models of systems with dissipation are based on the superposition of mechanical and thermodynamic Lagrangians. To obtain a mathematical description of dissipative systems it is proposed to use the field theory as applied to the thermodynamics of dissipative processes within the framework of the Lagrange formalism. The Euler-Lagrange equations are obtained for the Stokes and Coulomb friction models. As it was referred to the research results obtained there is possibility of accounting the energy dissipation in the Lagrange formalism. The mathematical models proposed describe dynamic processes in heterogeneous structures with friction based on the Euler-Lagrange theory. There are presented mathematical transformations that allow transition from models based on the Lagrange formalism to models based on Newtonian mechanics
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32

Moiseenko, R. P., and O. O. Kondratenko. "LAGRANGIAN METHOD FOR ALGORITHM OPTIMIZATION OF RIBBED THIN PLATES." Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture, no. 1 (April 13, 2018): 140–47. http://dx.doi.org/10.31675/1607-1859-2018-20-1-140-147.

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The paper presents two iteration algorithms for the equation solution using the method of Lagrange multipliers. It is shown that these iteration algorithms do not converge. For comparison, we use the optimum parameters of a ribbed plate obtained by other methods. The proposed method is based on the specific properties of optimality of ribbed plates formulated as a result of the Lagrange equation analysis. These optimum parameters satisfy each of Lagrange equations. The solution of these equations shows that optimization of ribbed plates is possible only with the use of specific optimality properties.
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33

De la Peña, Luis, Ana María Cetto, and Andrea Valdés-Hernández. "Power and beauty of the Lagrange equations." Revista Mexicana de Física E 17, no. 1 Jan-Jun (January 28, 2020): 47. http://dx.doi.org/10.31349/revmexfise.17.47.

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The Lagrangian formulation of the equations of motion for point particles isusually presented in classical mechanics as the outcome of a series ofinsightful algebraic transformations or, in more advanced treatments, as theresult of applying a variational principle. In this paper we stress two mainreasons for considering the Lagrange equations as a fundamental descriptionof the dynamics of classical particles. Firstly, their structure can benaturally disclosed from the existence of integrals of motion, in a waythat, though elementary and easy to prove, seems to be less popular--or less frequently made explicit-- than others insupport of the Lagrange formulation. The second reason is that the Lagrangeequations preserve their form in \emph{any} coordinate system --even in moving ones, if required. Their covariant nature makes themparticularly suited to deal with dynamical problems in curved spaces orinvolving (holonomic) constraints. We develop the above and related ideas inclear and simple terms, keeping them throughout at the level of intermediatecourses in classical mechanics. This has the advantage of introducing sometools and concepts that are useful at this stage, while they may also serveas a bridge to more advanced courses.
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34

Ma, Zhichao, and Junxiang Xu. "Lagrange stability for asymptotic linear Duffing equations." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 102701. http://dx.doi.org/10.1063/5.0044864.

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In this paper, by Moser’s non-twist theorem, we prove the Lagrange stability of asymptotic linear Duffing equations under weaker nonlinear assumptions. Comparing with previous works, we avoid some assumptions, which are usually required to guarantee the twist condition.
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35

Kryński, Wojciech. "The Schwarzian derivative and Euler–Lagrange equations." Journal of Geometry and Physics 182 (December 2022): 104665. http://dx.doi.org/10.1016/j.geomphys.2022.104665.

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36

Lee, Eun-Hwi, and Young-Seoung Song. "STABILITY OF GENERALIZED EULER-LAGRANGE FUNCTIONAL EQUATIONS." Honam Mathematical Journal 29, no. 1 (March 25, 2007): 61–74. http://dx.doi.org/10.5831/hmj.2007.29.1.061.

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37

Kikuchi, Keiichi. "Extended Harmonic Mappings and Euler-Lagrange Equations." Geometry, Integrability and Quantization 17 (2016): 284–95. http://dx.doi.org/10.7546/giq-17-2016-284-295.

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38

Marsden, Jerrold E., Tudor S. Ratiu, and Jürgen Scheurle. "Reduction theory and the Lagrange–Routh equations." Journal of Mathematical Physics 41, no. 6 (June 2000): 3379–429. http://dx.doi.org/10.1063/1.533317.

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39

Wu, Jing, Zengyuan Guo, and Bai Song. "Application of lagrange equations in heat conduction." Tsinghua Science and Technology 14, S2 (December 2009): 12–16. http://dx.doi.org/10.1016/s1007-0214(10)70023-7.

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40

Vázquez, L., and S. Jiménez. "Conservative numerical schemes for Euler-Lagrange equations." Il Nuovo Cimento A 112, no. 5 (May 1999): 455–59. http://dx.doi.org/10.1007/bf03035857.

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41

Bourdin, Loïc, Jacky Cresson, Isabelle Greff, and Pierre Inizan. "Variational integrator for fractional Euler–Lagrange equations." Applied Numerical Mathematics 71 (September 2013): 14–23. http://dx.doi.org/10.1016/j.apnum.2013.03.003.

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42

Agrawal, Om Prakash. "Generalized Variational Problems and Euler–Lagrange equations." Computers & Mathematics with Applications 59, no. 5 (March 2010): 1852–64. http://dx.doi.org/10.1016/j.camwa.2009.08.029.

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43

García-Toraño Andrés, Eduardo, Tom Mestdag, and Hiroaki Yoshimura. "Implicit Lagrange–Routh equations and Dirac reduction." Journal of Geometry and Physics 104 (June 2016): 291–304. http://dx.doi.org/10.1016/j.geomphys.2016.02.010.

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44

Hamid, Muhammad, Muhammad Usman, Tamour Zubair, and Syed Tauseef Mohyud-Din. "Comparison of Lagrange multipliers for telegraph equations." Ain Shams Engineering Journal 9, no. 4 (December 2018): 2323–28. http://dx.doi.org/10.1016/j.asej.2016.08.002.

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45

Muriel, C., J. L. Romero, and P. J. Olver. "Variational C∞-symmetries and Euler–Lagrange equations." Journal of Differential Equations 222, no. 1 (March 2006): 164–84. http://dx.doi.org/10.1016/j.jde.2005.01.012.

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46

Cendra, Hernán, and Viviana A. Díaz. "Lagrange-d'alembert-poincaré equations by several stages." Journal of Geometric Mechanics 10, no. 1 (2018): 1–41. http://dx.doi.org/10.3934/jgm.2018001.

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47

Chen, Lu, and Jianhua Shen. "Lagrange stability for impulsive pendulum-type equations." Journal of Mathematical Physics 61, no. 11 (November 1, 2020): 112704. http://dx.doi.org/10.1063/1.5144320.

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48

Mollin, R. A. "Lagrange, central norms, and quadratic Diophantine equations." International Journal of Mathematics and Mathematical Sciences 2005, no. 7 (2005): 1039–47. http://dx.doi.org/10.1155/ijmms.2005.1039.

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We consider the Diophantine equation of the formx2−Dy2=c, wherec=±1,±2, and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. As a consequence, we achieve a completely general, simple, and elegant criterion for the central norm to be2in the simple continued fraction expansion ofD.
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49

Laubenbacher, Reinhard, Gary McGrath, and David Pengelley. "Lagrange and the Solution of Numerical Equations." Historia Mathematica 28, no. 3 (August 2001): 220–31. http://dx.doi.org/10.1006/hmat.2001.2316.

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50

Sfarti, Adrian. "The Euler-Lagrange Equations in Rotating Frames." European Journal of Applied Physics 5, no. 1 (February 10, 2023): 24–28. http://dx.doi.org/10.24018/ejphysics.2023.5.1.236.

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We are interested in deriving the Euler-Lagrange equations of motion in rotating frames of reference since these are the real-life conditions encountered in every day. Our paper is divided into two main sections, the first section deals with centrally rotating frame, the second section deals with the peripherally rotating frame of reference in the relativistic regime of speeds.
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